lmom.ub {lmomco} | R Documentation

## Unbiased Sample L-moments by Direct Sample Estimators

### Description

Unbiased sample L-moments are computed for a vector using the direct sample estimation method as opposed to the use of sample probability-weighted moments. The L-moments are the ordinary L-moments and not the trimmed L-moments (see `TLmoms`). The mean, L-scale, coefficient of L-variation (tau, LCV, L-scale/mean), L-skew (tau_3, TAU3, L3/L2), L-kurtosis (tau_4, TAU4, L4/L2), and tau_5 (TAU5, L4/L2) are computed. In conventional nomenclature, the L-moments are

hat{λ}_1 = mbox{L1} = mbox{mean, }

hat{λ}_2 = mbox{L2} = mbox{L-scale, }

hat{λ}_3 = mbox{L3} = mbox{third L-moment, }

hat{λ}_4 = mbox{L4} = mbox{fourth L-moment, }

hat{λ}_5 = mbox{L5} = mbox{fifth L-moment, }

hat{tau} = mbox{LCV} = λ_2/λ_1 = mbox{coefficient of L-variation, }

hat{tau}_3 = mbox{TAU3} = λ_3/λ_2 = mbox{L-skew, }

hat{tau}_4 = mbox{TAU4} = λ_4/λ_2 = mbox{L-kurtosis, and}

hat{tau}_5 = mbox{TAU5} = λ_5/λ_2 = mbox{not named.}

### Usage

    lmom.ub(x)

### Arguments

`x` | A vector of data values.

### Details

The L-moment ratios (tau, tau_3, tau_4, and tau_5) are the primary higher L-moments for application, such as for distribution parameter estimation. However, the actual L-moments (λ_3, λ_4, and λ_5) are also reported. This implementation of L-moment calculation requires a minimum of five data points.

### Value

An R `list` is returned.

`L1` | Arithmetic mean.
`L2` | L-scale—analogous to standard deviation.
`LCV` | coefficient of L-variation—analogous to coe. of variation.
`TAU3` | The third L-moment ratio or L-skew—analogous to skew.
`TAU4` | The fourth L-moment ratio or L-kurtosis—analogous to kurtosis.
`TAU5` | The fifth L-moment ratio.
`L3` | The third L-moment.
`L4` | The fourth L-moment.
`L5` | The fifth L-moment.
`source` | An attribute identifying the computational source of the L-moments: “lmom.ub”.

### Author(s)

W.H. Asquith

### Source

The Perl code base of W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

Wang, Q.J., 1996b, Direct sample estimators of L-moments: Water Resources Research, vol. 32, no. 12., pp. 3617–3619.

### See Also

`lmom2pwm`, `pwm.ub`, `pwm2lmom`, `lmoms`, and `lmorph`

### Examples

    lmr <- lmom.ub(c(123,34,4,654,37,78))
    lmorph(lmr)
    lmom.ub(rnorm(100))

[Package lmomco version 0.92 Index]